IsaPlanner

What is IsaPlanner?

IsaPlanner is a generic framework for
proof planning in the interactive theorem prover Isabelle. It
facilitates the encoding of reasoning techniques, which can be used to
conjecture and prove theorems automatically. The system provides an
interactive tracing tool that allows you to interact the proof
planning attempt. (see the screenshot of IsaPlanner being used
with Isabelle and Proof
General) It is based on the Isabelle
theorem prover and the Isar
language. The main proof technique written in IsaPlanner is an inductive theorem prover based on Rippling. This is applicable within Isabelle's Higher Order Logic, and can easily be adapted to Isabelle's other logics.

The system now the main platform for proof planning
research in the Edinburgh mathematical reasoning group, and its
development is being continued by Lucas Dixon and Moa Johansson in the mathematical reasoning
group, at the University of Edinburgh.

If you would like to help, become involved in this
project, or work in collaboration, please feel free to contact: Lucas Dixon. There is also an IsaPlanner google group/email
list to which announcements will be sent and where you are welcome
to ask questions and discuss issues relating to proof planning and
IsaPlanner.

IsaPlanner Projects

The following list briefly describes the projects using IsaPlanner
that are currently in progress. If you know of any additional projects
or would like to start a new one using IsaPlanner, then please let us
know by emailing lucas.dixonated.ac.uk.

A Framework for Rippling We have developed a
framework for rippling in IsaPlanner that allows easy
experimentation with various modification to rippling. This
primarily allows experiments with different search strategies and
measures. The result is the provision of various rippling tactics
for Isabelle. This is a dynamic varient of rippling and supports
higher order logics.

An Inductive Theorem Prover We are using IsaPlanner
to provide an inductive theorem proving tactic for Isabelle.

Case SplittingExperiments with including case-splitting for if- and case-statements within rippling.

Lemma Discovary
Discovering unknown lemmas and theorems, generalisations, case-splits and other so called eureka steps, are major challenges for automated theorem proving. The project concerns automated discovary of lemmas which has generally been assumed that lemma discovery requires user intervention.

The Generation of Natural Language from IsaPlanner
Traces/Proof PlansFollowing the MSc project of Marianthi
Alexoudi we interested in integrating and extending her work on the
generation of natural language proofs from IsaPlanner traces and proof
plans.

Integration of IsaPlanner with Proof GeneralWe
are looking into ways to integrate proof planning with interactive
theory development and in particular considering how the PGIP protocal
can be extended to support such interactions. We will use to provide
interactive tools in the latest version of Proof General.

Deductive Synthesis of Induction SchemesWe are
interested in extending IsaPlanner to support the automatic derivation
of induction schemes duing the process of a deductive synthesis
proof. This includes porting the Dynamis system from LambdaClam to
IsaPlanner.

Projects Using IsaPlanner Technology

Isabelle
- rewriting using Zippers provides the basis for the substitution
tactic of Isabelle. This provides controlled for equational reasoning
which can occur under lambda abstractions. This has been used
in the L4
verification project and also in EPSRC grants GR/S01771/01,
GR/R01156/01, GR/S76328/01, GR/S25388/01, EP/E005713/1, GR/R01156/01,
GR/N64571/01, GR/T11715/01, EP/C510712/1, EP/F036345/1, GR/N37414/01.

Quantomatic
- A system for reasoning about quantum information; this uses the
name-management libraries of IsaPlanner to develop tools for working
with graphs that represent compact closed categories and which can be
used for symbolic evaluation of quantum processes. EPSRC grants using
this include: EP/E045006/1, EP/D072786/1, EP/E005713/1

IsaCoSy
- A system developed by Moa Johansson for her PhD project on automated
discovery of inductive lemmas, funded by EPSRC grant
EP/P501407/1. This uses the inductive theorem prover in IsaPlanner and
extends it using lemma-speculation critics as well other other lemma
discovary techniques.